Tens of thousands of children face being plunged into poverty by government plans to lower the household benefit cap, leaked advice to ministers shows.

The reduction in the upper limit of what families will now be able to claim annually from £26,000 to £23,000 was announced in Wednesday’s Queen’s speech.

Ministers claim changes to the cap contained in the forthcoming employment and welfare benefits bill will deliver fairness for the taxpayer “while continuing to provide support for those in greatest need”.

But an internal government assessment, seen by the Guardian, shows that if parents are unable to find extra work the policy will put 40,000 more children on or below the official poverty line, on top of the 50,000 already affected under the current rate.

Marked “sensitive” and sent to the work and pensions secretary, Iain Duncan Smith, two weeks after the general election, the civil service memo forecasts that “around 40,000 more ... children might in the absence of any behaviour change, find themselves in poverty as a result of reducing the cap to £23,000”.

“If these families respond to the cap by making behaviour change, for example moving into work, they are likely to see themselves and their children move out of relative poverty,” the civil service author adds.

Commenting on the leak, the Department for Work and Pensions said: “As the document itself makes clear, these figures do not take into account a key impact of the cap: that it incentivises people to move into work and improve their lives.”

The leak has emerged as housing associations forecast that, under the lower cap level, they will have to deal with a dramatic spike in rent arrears, evictions and homelessness, and will no longer be able to offer homes to jobless low-income families.

Social landlords, whose traditional mission has been to house the poor, say lowering the cap will make it economically risky for them to house all benefit-dependent families, and will undermine their plans to build more affordable homes.

Modelling by the National Housing Federation (NHF) indicates that on top of the 59,000 households already affected, a further 90,000 households across private and social sectors in England will have their income reduced by the new cap.

Detailed calculations by two housing associations, Moat and Sovereign, show that the lower cap level will make all three-bed affordable rented homes and some two-bed homes instantly unaffordable to capped tenants in a corridor stretching through Tory heartlands from Thanet and Basildon to Reading and Winchester.

Elizabeth Austerberry, the chief executive of Moat, said: “These people are not going to go away. Where are they going to live?”

The same estimates show reducing the maximum amount a jobless household can draw in benefits to £440 a week will lead to those affected typically losing around £65 a week in income, but in some cases as much as £100 a week.

“Potentially we are looking at evictions and homelessness. People affected will drift out of London to places where there is less chance of getting work,” Austerberry said.

She added that the cap would severely hinder associations’ plans to meet the government’s target of building 275,000 more affordable homes. “At a time when affordable housing is desperately needed, the policy will impact significantly on our ability to deliver housing under the current model.”

Tony Stacey, chair of Placeshapers, a group of 115 housing associations, said: “Many associations, faced with an increased risk profile, may decide they can no longer take the chance of letting homes to larger families on benefits.

“They may decide to stop developing larger homes. Placeshaper associations are committed to working with our local authority partners to find solutions. We do not want to turn our backs on the poor. And it’s not just us – private landlords will be similarly affected. The impact this will have on homelessness is truly worrying.”

Ian Gilders, director of business intelligence at Sovereign, said the cap meant social landlords would no longer be able to accept all nominations made from council waiting lists: “Housing associations will say to councils, ‘We would like to help, but with this family, under this benefit system, we can’t help.’”

The leaked DWP memo warns that it is vital ministers increase the amount of temporary cash help to capped tenants to prevent immediate eviction. However, the DWP cut the discretionary housing payment budget, which also covers households affected by the bedroom tax, from £165m to £125m from April.

A spokesperson for the government accused housing associations of “scaremongering” and claimed the cap had encouraged people to get a job.

The government believes that the principle of the cap is popular with voters. In January the prime minister, David Cameron, said the benefit cap “tells you everything you need to know about our values”.

The latest official figures show 59,000 households were hit by the £26,000 cap in the 22 months since its April 2013 introduction. Work and Pensions research from December found that 11% of households just below the cap level moved into work. This figure rose marginally to 15.7% for households who were capped.

A DWP qualitative impact study into the cap published that same month showed most capped tenants struggled to afford basic necessities and often went without food or borrowed cash from loan sharks, while a quarter reported being under threat of eviction as a result of running up rent arrears due to the cap.